# Coupled Variational Autoencoder

arXiv: https://arxiv.org/abs/2306.02565 · HTML: https://mlsanity.com/paper/2306.02565/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 30 of 30)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [VideoGPT: Video Generation using VQ-VAE and Transformers](https://mlsanity.com/paper/2104.10157/) (2021)
- [Conditional Variational Autoencoder with Adversarial Learning for End-to-End Text-to-Speech](https://mlsanity.com/paper/2106.06103/) (2021)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [Semi-Supervised Learning with Deep Generative Models](https://mlsanity.com/paper/1406.5298/) (2014)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Generative Modeling with Optimal Transport Maps](https://mlsanity.com/paper/2110.02999/) (2021)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Molecular generative model based on conditional variational autoencoder for de novo molecular design](https://mlsanity.com/paper/1806.05805/) (2018)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [A Contrastive Learning Approach for Training Variational Autoencoder Priors](https://mlsanity.com/paper/2010.02917/) (2020)
- [SOM-VAE: Interpretable Discrete Representation Learning on Time Series](https://mlsanity.com/paper/1806.02199/) (2018)
- [Towards Deeper Understanding of Variational Autoencoding Models](https://mlsanity.com/paper/1702.08658/) (2017)
- [Discriminator Rejection Sampling](https://mlsanity.com/paper/1810.06758/) (2018)
- [Dirichlet Variational Autoencoder](https://mlsanity.com/paper/1901.02739/) (2019)
- [Variational Autoencoder with Implicit Optimal Priors](https://mlsanity.com/paper/1809.05284/) (2018)
- [Multi-Stage Variational Auto-Encoders for Coarse-to-Fine Image Generation](https://mlsanity.com/paper/1705.07202/) (2017)

## Built on by (most cited first, 6 of 6)

- [Paired Wasserstein Autoencoders for Conditional Sampling](https://mlsanity.com/paper/2412.07586/) (2024)
- [Var-JEPA: A Variational Formulation of the Joint-Embedding Predictive Architecture - Bridging Predictive and Generative Self-Supervised Learning](https://mlsanity.com/paper/2603.20111/) (2026)
- [On Kernel-based Variational Autoencoder](https://mlsanity.com/paper/2405.12783/) (2024)
- [Diff-PCC: Diffusion-based Neural Compression for 3D Point Clouds](https://mlsanity.com/paper/2408.10543/) (2024)
- [MixFlow: Mixed Source Distributions Improve Rectified Flows](https://mlsanity.com/paper/2604.09181/) (2026)
- [A Multi-stage Constrained Optimization Framework for Data-driven Problems](https://mlsanity.com/paper/2607.23480/) (2026)

## Abstract (arXiv)

Variational auto-encoders are powerful probabilistic models in generative tasks but suffer from generating low-quality samples which are caused by the holes in the prior. We propose the Coupled Variational Auto-Encoder (C-VAE), which formulates the VAE problem as one of Optimal Transport (OT) between the prior and data distributions. The C-VAE allows greater flexibility in priors and natural resolution of the prior hole problem by enforcing coupling between the prior and the data distribution and enables flexible optimization through the primal, dual, and semi-dual formulations of entropic OT. Simulations on synthetic and real data show that the C-VAE outperforms alternatives including VAE, WAE, and InfoVAE in fidelity to the data, quality of the latent representation, and in quality of generated samples.